WB JEE 2022 | Differential Equations Question 36 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation

$${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$ into the form $${{{d^2}y} \over {d{z^2}}} + ky = 0$$ then k is equal to

$$-$$4

$$-$$2

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{\prime}\equiv{{{dx}\over {dy}}},y^{\prime\prime}\equiv{{{d^2}y\over {dx^2}}}$$

y² + xy'² $$-$$ yy' = 0

xyy'' + xy'² $$-$$ yy' = 0

yy' + xy'² $$-$$ xy' = 0

x²y' + xy'' $$-$$ 3y = 0

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive constant).

$$k{e^{{x^2}/2}}$$

$$k{e^{{y^2}/2}}$$

$$k{e^{{x^2}}}$$

$$k{e^{{y^2}}}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is

0.5

0.3

$$-$$ 0.2

$$-$$ 0.5

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